Question 1205486
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The container is a cone; and the water in the container forms a cone that is similar to the whole container.<br>
So there is no need in this problem to bother with the formula for the volume of a cone.  By a powerful general principle for similar figures, if the scale factor (ratio of linear measurements) between two similar figures is A:B, then the ratio of area measurements between the figures is A^2:B^2, and the ratio of volume measurements between the figures is A^3:B^3.<br>
In this problem, the ratio of volumes of the two cones is 1:2, so the ratio of linear measurements is {{{1:root(3,2)}}}<br>
The height of the large cone (the container) is 16cm, so the height of the small cone (the depth of the water) is {{{16/root(3,2)}}} = 12.70cm to 2 decimal places.<br>
ANSWER: 12.70cm<br>